Interesting Definition and 790 Threads

Hey guys, if the function f(x) has a special property that; f'(x) = f(x) g(x) Whats the easiest way to find the nth derivative of f(x) in terms of f(x), g(x) and g'(x)'s derivatives? The same problem rephrased is if q(x) is the logarithmic derivative of f(x), then what's the nth derivative...

Homework Statement Imagine that you are lost in the desert. You are equipped with a compass. You can use your compass to measure angles, but not the distances. There is a road (going from east to west) and you're going northwards. Suddenly, you spot a truck (on a road, going to west) at...

Homework Statement ~ Homework Equations center The Attempt at a Solution i can do part a. can you give me hints on part b and c?

On a test in multivariable calculus I came across, what I thought, was an interesting parabola. Figured I'd ask the forum because my professor is pretty unavailable. In parametric form it is, x=t+4 , y = (1/2)t^2 + 2 The reason I found it interesting is because t is always equal to...

So I've read the highest skydive occurred from a balloon and the entire jump lasted on the order of 10s of minutes. Heres my question: How the do you know where your going to land? The Earth rotates at ~1000mi per hour that's 12 mi per minute or 2.7 miles per 10 secs. So did these people use...

Comparing the average speed of a bunch of points with the individual points' speeds, I came across the following equation: \left(\frac{dx(t)}{dt}\right)^2 = \frac{1}{N^2} c^2 \sum_{i\neq j} \left(1-\frac{v_i(t) v_j(t)}{c^2}\right) where the v_i are the velocity vectors (3 dimensions) of the...

I found a pretty interesting question on the net. Can anyone please attempt at answering it? This is NOT a Homework question. I haven't reached this portion in my school, but I'm pretty interested in solving it. A German childrens' book, "Der Struwwelpeter" show as humor various misbehavior...

I've been working on this problem and would like some help or any hints. Give an example of a nonempty set A subset of R such that A = br(A) = Lim(A) = Cl(A), where br(A) denotes the boundary points of A, Lim(A) denotes the limit points of A and Cl(A) denotes the closure of A. I've tried...

I've been working on this problem and would like some help or any hints. Give an example of a nonempty set A subset of R such that A = br(A) = Lim(A) = Cl(A), where br(A) denotes the boundary points of A, Lim(A) denotes the limit points of A and Cl(A) denotes the closure of A. I've tried...

Homework Statement From 52 cards we draw one .Whats the probability that the drawn card is divisible by 4 Now : in my notebook its 12/52=3/13 .But shouldn't it be 13/52 ? BECAUSE clearly if we multiply 13 *4=52 Same problem : Whats the probability that of 52 cards I draw one that is...

Is there a proof or way of proving that all even numbers (taking into account the definition of an even number as n=2k) end in 0,2,4,6, or 8?

Take a prime[n] and double it, i.e., e.g., Pn (n=7) so prime[7] is 17, doubled to 34. Take all unique arrangements of two primes from P2 (3) to P7 (17): {3,3}, {3,5}, {5,5}, ..., {13, 17}, {17,17} Add the pairs together, e.g., {3,3} = 3 + 3 = 6 Now eliminate duplicates, i.e., {5,5} and {3,7}...

Stuff i find interesting in some way! K this is a thread I'm making to show u some things that i find interesting and hopefully some of u will find it interesting too.. It will be updated on regular basis with new interesting articles from various sources so stay tuned.. First article is...

So I'm thinking that for grad school I might like to get into some computational simulations and modeling. The reason for this is I'm not sure if I'll want to stay in Physics after grad school and being good with computers and modeling and such I think will give me a lot of options outside of...

Hi guys, Homework Statement how do i solve (or approximate if not solvable) this integral \int\int e^{-\alpha(|\vec{r}_1-\vec{r}_2|-r_0)^2} d^3\vec{r}_1 d^3\vec{r}_2 \alpha>0 Homework Equations none The Attempt at a Solution none

Linear Polarisability \alpha_{ij} is the amplitude of the electric field induced in the molecule in the i direction given a unit amplitude field in the j direction, hence E_i^{induced} = \alpha_{ij} E_j^{incident} (observing summation convention) Extending this physical...

I have spent hours and hours trying to solve a problem until reaching a dead point. I don't know how to solve, simplify, or proceed next with the following PDE: m \frac{\partial^2 x}{\partial t^2} + 2 \frac{\partial m}{\partial t} \frac{\partial x}{\partial t} + x \frac{\partial^2...

Well since we will never see something go into a black hole, won't we see everything the black hole tries to swallow around it? So wouldn't it be possible to see a black hole since a bunch of things would be around the event horizon. Answers are appreciated.

I've come up with a scenario which seems to be something of a paradox to me: Imagine, if you will, two similar rotating objects orbiting each other at a fixed distance, sharing the same rotational plane. These two objects now experience acceleration to some fixed speed along their shared axis...

Long back (not so much long back), when I was first introduced to complex numbers, my mind was flooded with strange and interesting curiosities (as they appeared to me!), rather ideas. Of course this realm of mathematics is, as the mathematicians are fond of saying, is remarkably beautiful. As I...

A friend asked me for an interesting way to destroy a boxful of flashcards for a video scholarship. Being almost the 4th of July, I mentioned making some kind of fireworks out of them, but I want to give him something a little more... safe and legal. I tried looking on Google for chemical...

I found an interesting limit: any ideas? :)

Happened to go to a group of fundamental pentecostal families for a music night, where we spent the evening singing pop songs. We were singing a few devotional songs too, as expected. I randomly sang a virgin Mary devotional song, and everyone started looking at me as if I spoke some profanity...

Hello all, I am a fourth year at uni, getting my degree in applied mathematics with a minor in computing. I've taken classes in physics (electromagnetism and circuits) and lots of programming... and recently landed a co op position as an electrical engineer in a large (14,000+ people) medical...

So I was doing some FE work (w/ NASTRAN) to determine the stiffness in all 6 DOF of a model bolted to another model. To characterize the bolted interfaces I attached surface nodes within the bolt frustums to rigid body elements (RBE2). Then, these RBE2s were connected with a directional...

http://www.nbc.com/americas-got-talent/video/week-1-night-2/1232101/ watch starting around 5:35...' explanation??

Recently, I have come across some interesting studies of sound called 'Cymatics'. I was curious in how the modern scientific community views this intriguing field of research... Can anyone help to enlighten me on the subject?

Suppose I put 1 kg of -10-degree ice in a 1 m^3 vacuum chamber. How much heat do I have to add to turn all of the ice into vapor at 100 degrees Celsius? This seems like a ridiculously simple problem, but I realized I've no idea how to solve it. First of all, ice sublimates in a vacuum...

Homework Statement Suppose f is continuous and F(x)=\int_a^x f(t)dt bounded on [a,b). Given g>0, g'\geq 0 and g' locally integrable on [a,b) and lim_{ x\rightarrow b^-} g(x) = infinity. prove for p>1 \displaystyle{lim_{ x\rightarrow b^-} \frac{1}{[g(x)]^p} \int^x_a f(t)g(t)dt = 0}...

I hate a piece-wise function f(x)= [ 1 if 0 </eq x </1 [ 0 if 1 < x < 2 [ -2x+4 if x >/eq 2 If I let F(x)= integral (from 0->x) f(t) dt, how can i find a formula for F(x) without using integrals? I think it may have something to do with the 2nd definition of the...

Suppose that a set S has the property that all of its members are integers and that the average of any 3 of its members is not an integer. What is the maximum number of elements that S may have?

Homework Statement Consider a momentum distribution such that: f(\overline{p}) = (2*\pi*k*T*m)^(3/2)*exp(-p^2/(2*m*k*T))*(1+\epsilon*cos(\alpha) where \alpha is the angle between \overline{p} and \alpha a) what is the expectation value associated with U = <V_x> + <V_y> + <V_z> b)...

While messing around with the Schrödinger equation on paper, I found an interesting, elegant way of expressing it. Let P be the probability density |\Psi |^2, and let \vec Q be a real-valued vector field. \vec F is a vector field describing the forces acting on the system when in a given...

Hi, what I did to try to find prime numbers was this (in a computer program) Starting from 2, I set off a sine wave that has an amplitude=0 for every even number and an amplitude=1 for every odd number. What we are looking for, then, are the portions of the sine wave where the derivative...

I am doing a report and presentation on Erwin Schrödinger in my physics class and I want it to be exciting and interesting. Does anyone have and interesting facts about this great scientist? Not just FACTS, but INTERESTING facts! I have heard that he was quite the ladies man... Thanks! ~Matt

I am still far too much of a newbie to be able to intelligently speak on any of the items listed in this website, but it all seems very interesting. Will anyone comment on the veracity of this article, and if it's really as "cutting edge" as they make it sound? I find item #3 particularly...

I'm in my 4th year of a physics program, and I've got some serious freedom choosing courses now. Has anyone taken graph theory? I've got a basic idea what it is, but no clue how difficult it might be. Any other good math courses to take as an option that won't bee too difficult? For...

\lim_{n\to infinity}{{(\sqrt{n^{2}+n+1}})-[{(\sqrt{n^{2}+n+1}})]} wer [.] is GIF how will u solve this one

I'm afraid the template for homework help doesn't quite apply here since my problem is the lack of a problem in itself. I'm an International Baccalaureate student, and I've decided to do a research topic (about 4000 words) on physics. I need help with this. I'm looking for suggestions for...

hey everyone, My class was thinking about buying a present for our physics professors. We are currently studying for A-Levels. as it is his last year of teaching. So I just wish to tell you the situtation -our prof is graduated in physics and maths -our prof told us that once he got...

I am having a tank at the bottom of which a pump suction line is connected.. there is another parralel line to that bottom line which is coming from another tank and open to atmospheric pressure. Please note that this second pipe is connected to the bottom pipe; not to the first tank...

Hello, I have a question Lets say you have a container of water that weighs 10 pounds including the water/container material and u have a 5 pound object that can float quite easily in that water and u attach a piece of string to that object to the bottom of the container of water to the...

A 2 gram Magnesium (Mg) ribbon is burnt in air . The burnt ribbon is collected and weighed. Would it be greater than 2 grams or lesser?

I found this experiment on YouTube, and its about interference pattern variation in a vertically spinning interferometer.. http://www.youtube.com/watch?v=7T0d7o8X2-E&feature=related

"Did You Know..." Our department has bulletin boards for each faculty member; I'm looking for ideas on what to put on mine. The idea is for each member to advertise themselves to the (undergraduate) student body- not just majors, but any student that wanders by. My wife came up with a 'Did...

Some interesting brainteasersStarterI used Some interesting brainteasers Starter I used factorials for this one, but it will be interesting to see how you attempt your answer. Head Scratcher These questions are designed so that anybody above the age of about 13 can answer...

Some interesting brainteasers Starter I used factorials for this one, but it will be interesting to see how you attempt your answer. Head Scratcher These questions are designed so that anybody above the age of about 13 can answer them without much mathematical experience. If...

Hello, I have a few questions that I have made myself, but I don't know how to answer them. 1) Say that there is an isosceles triangle ABC. Two of the equal angles are 1/∞. What is the other angle? 2) Is a sphere really a sphere if you can draw a tangent to it? 3) Assume that there...

I have some very vexing questions regarding light. We seem to know so little about it. 1. What happens to light when it is not traveling ? 2. Does it accelerate in reaching C ? If not does it "jump" to C ? 3. Can it be destroyed ? If not it seems to me that the amount of light in the...

suppose i want to find the following integral: 7 \intx dx 3 now suppose for some demented reason i decided not to do it straightforward and get (49-9)/2=20 instead i use the substitution x=u2+4u+5 giving u1 \int(u2+4u+5)(2u+4)du u0 u1 \int2u3+12u2+26u+20 du u0 the indefinite integral is...